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1. Number Properties2. Fractions, Decimals, & Percents3. Equations, Inequalities, & VICs4. Word Translations5. Geometry6. Critical Reasoning7. Reading Comprehension8. Sentence Correction

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Word Translations

4Guide

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Bonus Question Bank for Word Translations

See page 7 for details.

How Our GMAT Prep Books Are Different

1. ALGEBRAIC TRANSLATIONS: Translation Techniques, Using Charts, Prices and Quantities, Hidden Constraints

2. RATES & WORK: RTD Charts, Matching Units, Multiple RTD Problems, Average Rate, Basic Work, Working Together, Population, Exponential Growth/Decay (Advanced)

3. RATIOS: Labels, Proportions, Unknown Multipliers, Multiple Ratios

4. COMBINATORICS: Fundamental Counting Principle, Factorials, Anagrams, Multiple Arrangements, Arrangements with Constraints, Combination and Permutation Formulas (Advanced), Disguised Combinatorics (Advanced)

5. PROBABILITY: And vs. Or, 1 – x Shortcut, Domino Effect, Probability Trees, Combinatorics and Probability (Advanced), Combinatorics and Domino Effect (Advanced), Reformulating Difficult Problems (Advanced)

6. STATISTICS: Average Formula, Evenly Spaced Sets, Weighted Averages, Median, Standard Deviation, Shortcuts (Advanced)

7. OVERLAPPING SETS: Double-Set Matrix, Sets & Percents, Sets & Algebraic Representation, Venn Diagrams

8. MINOR PROBLEM TYPES: Optimization, Grouping, Scheduling, Computation, Graphing

TH

IRD

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ITIO

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T Strategy Guide

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Part of 8-Book Series

What's Inside This Guide

• Clear explanations of fundamental principles.• Step-by-step instructions for important techniques.• Advanced sections covering the most difficult topics.• In-Action practice problems to help you master the concepts and methods.• Topical sets of Official Guide problems listed by number (problems published separately by GMAC) to help you apply your knowledge to actual GMAT questions.• One full year of access to 6 Computer Adaptive Practice Exams and Bonus Question Bank.

• Not just pages of guessing tricks• Real content, real structure, real teaching• More pages per topic than all-in-1 tomes

• Challenges you to do more, not less• Focuses on developing mastery• Covers the subject thoroughly

WORDTRANSLATIONS

This comprehensive guide analyzes the GMAT’s complexword problems and provides structured frameworks forattacking each question type. Master the art of translatingchallenging word problems into organized data.

Math Strategy Guideg

Word Translations GMAT Strategy Guide, Third Edition

10-digit International Standard Book Number: 0-9818533-7-413-digit International Standard Book Number: 978-0-9818533-7-6

Copyright © 2008 MG Prep, Inc.

ALL RIGHTS RESERVED. No part of this work may be reproduced or used in anyform or by any means—graphic, electronic, or mechanical, including photocopying,recording, taping, Web distribution—without the prior written permission of the pub-lisher, MG Prep Inc.

Note: GMAT, Graduate Management Admission Test, Graduate ManagementAdmission Council, and GMAC are all registered trademarks of the GraduateManagement Admission Council which neither sponsors nor is affiliated in any waywith this product.

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Number Properties (ISBN: 978-0-9818533-4-5)

Fractions, Decimals, & Percents (ISBN: 978-0-9818533-2-1)

Equations, Inequalities, & VICs (ISBN: 978-0-9818533-1-4)

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Geometry (ISBN: 978-0-9818533-3-8)

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5

September 30th, 2008

Dear Student,

Thank you for picking up one of the ManhattanGMAT Strategy Guides—we hope that it refreshes yourmemory of the junior-high math that you haven’t used in years. Maybe it will even teach you a new thingor two.

As with most accomplishments, there were many people involved in the various iterations of the book thatyou’re holding. First and foremost is Zeke Vanderhoek, the founder of ManhattanGMAT. Zeke was a lonetutor in New York when he started the Company in 2000. Now, eight years later, MGMAT has Instructorsand offices nationwide, and the Company contributes to the studies and successes of thousands of studentseach year.

These 3rd Edition Strategy Guides have been refashioned and honed based upon the continuing experi-ences of our Instructors and our students. We owe much of these latest editions to the insight provided byour students. On the Company side, we are indebted to many of our Instructors, including but not limitedto Josh Braslow, Dan Gonzalez, Mike Kim, Stacey Koprince, Jadran Lee, Ron Purewal, Tate Shafer, EmilySledge, and of course Chris Ryan, the Company’s Lead Instructor and Director of CurriculumDevelopment.

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1. ALGEBRAIC TRANSLATIONS

In Action Problems

Solutions

2. RATES & WORK

In Action Problems

Solutions

3. RATIOS

In Action Problems

Solutions

4. COMBINATORICS

In Action Problems

Solutions

5. PROBABILITY

In Action Problems

Solutions

6. STATISTICS

In Action Problems

Solutions

7. OVERLAPPING SETS

In Action Problems

Solutions

8. MINOR PROBLEM TYPES

In Action Problems

Solutions

9. STRATEGIES FOR DATA SUFFICIENCY

Sample Data Sufficiency Rephrasing

10. OFFICIAL GUIDE PROBLEM SETS

Problem Solving List

Data Sufficiency List

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ManhattanGMATPrepthe new standard

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TABLE OF CONTENTS

11

21

23

29

45

47

53

59

61

65

79

81

89

101

103

109

121

123

125

135

137

141

147

149

153

157

163

166

167

ALGEBRAICTRANSLATIONS

g WORD TRANSLATIONS

Chapter 1of

In This Chapter . . .

• Algebraic Translations

• Translating Words Correctly

• Using Charts to Organize Variables

• Prices and Quantities

• Hidden Constraintsg

ALGEBRAIC TRANSLATIONS STRATEGY

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Be sure to make a noteof what each variable

represents. If you can,use meaningful letters as

variable names.

Chapter 1

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Algebraic TranslationsTo solve many word problems on the GMAT, you must be able to translate English intoalgebra. You select variables and variable expressions to represent unknown quantities. Thenyou write equations to state relationships between the unknowns and any known values.Once you have written one or more algebraic equations to represent a problem, you cansolve them to find any missing information.

A candy company sells premium chocolates at $5 per pound and regular

chocolates at $4 per pound. If Barrett buys a 7-pound box of chocolates that

costs him $31, how many pounds of premium chocolates are in the box?

To solve this problem, simply translate the words into algebraic equations:

Step 1: Assign variables.If possible, designate only one variable, and use it to represent all unknown information.

Almost every word problem will refer to more than one quantity, but most solutions workbest when they involve only one variable. Therefore, you should try to express all quantitiesin terms of a single variable—ideally, the “Ultimate Unknown” that the problem is askingfor, but only if that Ultimate Unknown is a simple quantity.

In the problem above, the pounds of premium and regular chocolate must add to 7.Therefore, if you know one of the weights in pounds, you can subtract from 7 to find theother. We can assign the following:

p = number of pounds of premium chocolate= number of pounds of regular chocolate

You should also note that p is the Ultimate Unknown that the problem wants you to find. Agood way to remind yourself is to write down “p = ?” on your paper.

Time is short during the GMAT, so you should not waste valuable seconds searching forone-variable expressions if you cannot nail them down right away. Instead, try using addi-tional variables—but with an eye to finding substitutions that will ultimately reduce thenumber of variables to just one. In the chocolate problem, you could assign the following:

p = number of pounds of premium chocolater = number of pounds of regular chocolate

These two variables are related by the equation . Since the question is ultimatelyabout p, you want a substitution that will eliminate r. Therefore, solve this equation for r:

Thus, there are p pounds of premium chocolate and pounds of regular chocolate, andthe problem has been successfully reduced to one variable. By the way, you could have usedthe letters x and y to represent the pounds of premium and regular chocolate, but if you usep and r, you will never forget which is which. Use meaningful letters if you can.

7 p−

7r p= −

7p r+ =

7 p−

ALGEBRAIC TRANSLATIONS STRATEGY

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Most algebraic translation problemsinvolve only the 4 simplearithmetic processes:addition, subtraction,multiplication, and division. Look for totals,differences, products andratios.

Chapter 1

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Step 2: Write equation(s).If you are not sure how to construct the equation, begin by expressing a relationshipbetween the unknowns and the known values in words. For example, you might say:

“The total cost of the box is equal to the cost of the premium chocolates plus thecost of the regular chocolates.”

You might even write down a “Word Equation,” halfway between English and algebra:

“Total Cost of Box = Cost of Premiums + Cost of Regulars”

Then, translate the verbal relationship into mathematical symbols. Use another relationship,Total Cost = Unit Price × Quantity, to write the terms on the right hand side. For instance,the “Cost of Premiums” in dollars = ($5 per pound)(p pounds) = 5p.

Note that many word problems, including this one, require a little basic background knowl-edge to complete the translation to algebra. Here, to write the expressions 5p and 4(7 − p),you must understand that Total Cost = Unit Price × Quantity. In this particular problem, thequantities are weights, and the units of those quantities are pounds.

Although the GMAT requires little factual knowledge, it will assume that you have mas-tered the following relationships:

• Total Cost = Unit Price × Quantity purchased• Total Sales or Revenue = Unit Price × Quantity sold (essentially the same relation)• Profit = Revenue − Cost• Distance = Rate × Time (this relation will be covered in the next chapter)

Step 3: Solve algebraically.

Step 4: Evaluate the algebraic solution in the context of the problem.Once you solve for the unknown, look back at the problem and make sure you answer thequestion asked. In this problem, we are asked for the number of pounds of premiumchocolate in the box. This is the Ultimate Unknown. Notice that we wisely chose our vari-able p to represent the Ultimate Unknown. This way, once we have solved for p, there areno additional steps to take. If you use two variables, p and r, and accidentally solve for rinstead of p, you might choose 4 as your answer. This is why you should always note whatthe Ultimate Unknown is at the beginning of the problem (e.g., by writing “p = ?”).

31 5 4(7 )31 5 28 43

p pp p

p

= + −

= + −

=

= + −31 5 4(7 )p pThe totalcost of thebox

is equal to plus the cost of theregular chocolates

the cost ofthe premiumchocolates

ALGEBRAIC TRANSLATIONS STRATEGY

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Be ready to insert simpletest numbers to make

sure that your translationis correct.

Chapter 1

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Translating Words CorrectlyWhen you write equations representing relationships between variables—even if those rela-tionships are fairly simple—you must be careful to avoid writing the relationships back-

wards. For instance, if you see “A is half the size of B,” you should write , not the

wrong way around as . Likewise, “A is 5 less than B” is written as A = B − 5. This

relation is often incorrectly represented as A = 5 − B or as A − 5 = B.

Because the stakes are so high for each GMAT problem, it is often worth a quick checkwith easy numbers to see whether you have written a relationship in the correct direc-tion. For example, if you see “A is 5 less than B,” then select, say, A = 2 and B = 7 to sat-isfy that relationship. (Note that these numbers do not have to satisfy other conditionsgiven in the problem; their only purpose is to test the relationship you are looking at.)Trying these numbers in each of the three different re-writings of the equation yields

A = B − 5 � 2 = 7 − 5 Correct!A = 5 − B � 2 = 5 − 7 ? Incorrect!A − 5 = B � 2 − 5 = 7 ? Incorrect!

This quick testing will confirm that you have indeed written the correct form of an equa-tion, so that you can proceed with confidence. If you ever make these types of errors, thentake the time to perform these quick tests. Many incorrect answer choices on the GMAT arederived from mistakes just like these!

Note also the two uses of “less than.”“A is 5 less than B” turns into an equation with a subtraction: A = B − 5“A is less than B” turns into an inequality: A < B

The difference is whether you specify how much less than. “More than” works similarly.

Percents can be tricky:

“p is what percent of q?” turns into an equation with a new variable: .

Or you can write proportions: . Either way, you need to solve for x.

Finally, note that not all statements should be translated one word or phrase at a time. Sometranslations require you to view the statement as a whole to write an appropriate equation.For instance, if you see “Justina bought twice as many apples as bananas at the market,”then you should write A = 2B, not 2A = B (as you can check with easy numbers).

If you try to translate the equation word for word, you might get the incorrect version,because the word “twice” appears closer to “apples.” Or you might wrongly think that 2Ameans “two apples.” A represents the number of apples, which is larger than the number ofbananas, B. So we must multiply the number of bananas by 2 to get the number of apples:A = 2B is correct. The moral is this: always pay attention to the meaning of the sentence youare translating!

100p xq

=

100xp q⎛ ⎞= ⎜ ⎟

⎝ ⎠

=2A

B

=2B

A

ALGEBRAIC TRANSLATIONS STRATEGY

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The age chart does notrelate the ages of the individuals. It simplyhelps you to assign variables you can use towrite equations.

Chapter 1

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Using Charts to Organize VariablesWhen an algebraic translation problem involves several quantities and multiple relation-ships, it is often a good idea to make a chart to organize information.

One type of algebraic translation that appears on the GMAT is the “age problem.” Ageproblems ask you to find the age of an individual at a certain point in time, given someinformation about other people's ages at other times.

Complicated age problems can be effectively solved using an Age Chart. Such a chart helpsyou keep track of one person’s age at different times or several ages at one time.

8 years ago, George was half as old as Sarah. Sarah is now 20 years older

than George. How old will George be 10 years from now?

Step 1: Assign variables.Set up an Age Chart to help you keep track of the quantities. Put the different people inrows and the different times in columns. Then assign variables. You could use two variables(G and S), or you could use just one variable (G) and represent Sarah’s age as G + 20, sincewe are told that Sarah is now 20 years older than George. We will use the second approach.Either way, always use the variables to indicate the age of each person now (this way, youwill not confuse yourself ). Fill in the other columns by adding or subtracting time from the“now” column (for instance, subtract 8 to get the “8 years ago” column). Also note theUltimate Unknown with a question mark.

Step 2: Write equation(s).Write equations that relate the individuals' ages together. According to this problem, 8 yearsago, George was half as old as Sarah. Using the age expressions in the “8 years ago” column,we can write the following equation:

which can be rewritten as

Step 3: Solve algebraically.

Step 4: Evaluate the algebraic solution in the context of the problem.In this problem, we are asked to find George’s age in 10 years. In other words, G + 10 is theUltimate Unknown. Since George is now 28 years old, he will be 38 in 10 years. Theanswer is 38 years.

Note that if we had used two variables, G and S, we might have set the table up slightlyfaster, but then we would have had to solve a system of 2 equations and 2 unknowns.

2 16 1228

G GG

− = +

=

2 16 12G G− = +12

82

GG

+− =

8 years ago Now 10 years from now

George G − 8 G G + 10 = ?

Sarah G + 12 G + 20 G + 30

ALGEBRAIC TRANSLATIONS STRATEGY

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In a typicalPrice–Quantity problem,

you have two relation-ships. The quantities

sum to a total, and themonetary values sum to

a total.

Chapter 1

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Prices and QuantitiesMany GMAT word problems involve the total price or value of a mixed set of goods. Onsuch problems, you should be able to write two different types of equations right away.

1. Relate the quantities or numbers of different goods: Sum of these numbers = Total.2. Relate the total values of the goods (or their total cost, or the revenue from their sale):

Money spent on one good = Price × Quantity.Sum of money spent on all goods = Total Value.

The following example could be the prompt of a Data Sufficiency problem:

Paul has twenty-five transit cards, each worth either $5, $3, or $1.50. What

is the total monetary value of all of Paul’s transit cards?

Step 1. Define variablesThere are three quantities in the problem, so the most obvious way to proceed is to desig-nate a separate variable for each quantity:

x = number of $5 transit cardsy = number of $3 transit cardsz = number of $1.50 transit cards

Alternatively, you could use the given relationship between the three quantities (they sum to25) to reduce the number of variables from three to two:

number of $5 transit cards = xnumber of $3 transit cards = ynumber of $1.50 transit cards = 25 − x − y or 25 − (x + y)

Note that in both cases, the Ultimate Unknown (the total value of the cards) is not given avariable name. This total value is not a simple quantity; we will express it in terms of thevariables we have defined.

Step 2. Write equationsIf you use three variables, then you should write two equations. One equation relates thequantities or numbers of different transit cards; the other relates the values of the cards.Numbers of cards: x + y + z = 25

Values of cards: 5x + 3y + 1.50z = ? (this is the Ultimate Unknown for the problem)

If you have trouble writing these equations, you can use a table to help you. The columnsof the table are Unit Price, Quantity, and Total Value (with Unit Price × Quantity = TotalValue). The rows correspond to the different types of items in the problem, with one addi-tional row for Total.

In the Quantity and Total Value columns, but not in the Unit Price column, the individualrows sum to give the quantity in the Total row. Note that Total Value is a quantity of money(usually dollars), corresponding either to Total Revenue, Total Cost, or even Total Profit,depending on the problem’s wording.

ALGEBRAIC TRANSLATIONS STRATEGY

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You can use a table toorganize your approachto a Price–Quantityproblem. However, ifyou learn to write theequations directly, youwill save time.

Chapter 1

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For this type of problem, you can save time by writing the equations directly. But feel freeto use a table approach.

Notice that the numbers in the second and third columns of the table (Quantity and TotalValue) can be added up to make a meaningful total, but the numbers in the first column(Unit Price) do not add up in any meaningful way.

If you use the two-variable approach, you do not need to write an equation relating thenumbers of transit cards, because you have already used that relationship to write the expres-sion for the number of $1.50 cards (as 25 − x − y). Therefore, you only need to write theequation to sum up the values of the cards.

Values of cards: 5x + 3y + 1.50(25 − x − y) = ?

Simplify � 3.5x + 1.5y + 37.5 = ?

Here is the corresponding table:

All of the work so far has come just from the prompt of a Data Sufficiency question—youhave not even seen statements (1) and (2) yet! But this work is worth the time and energy.In general, you should rephrase and interpret a Data Sufficiency question prompt as muchas you can before you begin to work with the statements.

Unit Value × Quantity = Total Value

$5 cards 5 × x = 5x

$3 cards 3 × y = 3y

$1.50 cards 1.5 × 25 − x − y = 1.5(25 − x − y)

Total — 25 ?

Unit Price × Quantity = Total Value

$5 cards 5 × x = 5x

$3 cards 3 × y = 3y

$1.50 cards 1.5 × z = 1.5z

Total — 25 ?

ALGEBRAIC TRANSLATIONS STRATEGY

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ManhattanGMATPrep

When a variable indi-cates how many objects

there are, it must be awhole number.

Chapter 1

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Hidden ConstraintsNotice that in the previous problem, there is a hidden constraint on the possible quantitiesof cards (x, y, and either z or 25 − x − y). Since each card is a physical, countable object, youcan only have a whole number of each type of card. Whole numbers are the integers 0, 1,2, and so on. So you can have 1 card, 2 cards, 3 cards, etc., and even 0 cards, but you can-not have fractional cards or negative cards.

As a result of this implied “whole number” constraint, you actually have more informationthan you might think. Thus, you may be able to answer the question with less informationfrom the statements.

As an extreme example, imagine that the question is “What is x?” and that statement (1)reads “1.9 < x < 2.2”. If some constraint (hidden or not) restricts x to whole-number values,then statement (1) is sufficient to answer the question: x must equal 2. On the other hand,without constraints on x, statement (1) is not sufficient to determine what x is.

Recognizing a hidden constraint can be useful, not only on Data Sufficiency problems, butalso on certain Problem Solving problems. Consider the following example:

If Kelly received 1/3 more votes than Mike in a student election, which of the

following could have been the total number of votes cast for the two candi-

dates?

(A) 12

(B) 13

(C) 14

(D) 15

(E) 16

Let M be the number of votes cast for Mike. Then Kelly received M + (1/3)M, or (4/3)Mvotes. The total number of votes cast was therefore “votes for Mike” plus “votes for Kelly,”or M + (4/3)M. This quantity equals (7/3)M, or 7M /3.

Because M is a number of votes, it cannot be a fraction—specifically, not a fraction with a 7in the denominator. Therefore, the 7 in the expression 7M /3 cannot be cancelled out. As aresult, the total number of votes cast must be a multiple of 7. Among the answer choices,the only multiple of 7 is 14, so the correct answer is (C).

Another way to solve this problem is this: the number of votes cast for Mike (M) must be amultiple of 3, since the total number of votes is a whole number. So M = 3, 6, 9, etc. Kellyreceived 1/3 more votes, so the number of votes she received is 4, 8, 12, etc. Thus the totalnumber of votes is 7, 14, 21, etc.

Not every unknown quantity related to real objects is restricted to whole numbers. Manyphysical measurements, such as weights, times, or speeds, can be any positive number, notnecessarily integers. A few quantities can even be negative (e.g., temperatures, x- or y-coordi-nates). Think about what is being measured or counted, and you will recognize whether ahidden constraint applies.

IN ACTION

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ManhattanGMATPrep

Chapter 1

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ALGEBRAIC TRANSLATIONS PROBLEM SET

Problem SetSolve the following problems with the four-step method outlined in this section.

1. John is 20 years older than Brian. 12 years ago, John was twice as old as Brian.

How old is Brian?

2. Mrs. Miller has two dogs, Jackie and Stella, who weigh a total of 75 pounds. If

Stella weighs 15 pounds less than twice Jackie’s weight, how much does Stella

weigh?

3. Caleb spends $72.50 on 50 hamburgers for the marching band. If single burgers

cost $1.00 each and double burgers cost $1.50 each, how many double burgers

did he buy?

4. Abigail is 4 times as old as Bonnie. In 6 years, Bonnie will be twice as old as

Candice. If, 4 years from now, Abigail will be 36 years old, how old will Candice

be in 6 years?

5. United Telephone charges a base rate of $10.00 for service, plus an additional

charge of $0.25 per minute. Atlantic Call charges a base rate of $12.00 for serv-

ice, plus an additional charge of $0.20 per minute. For what number of minutes

would the bills for each telephone company be the same?

6. Ross is 3 times as old as Sam, and Sam is 3 years older than Tina. 2 years from

now, Tina will drink from the Fountain of Youth, which will cut her age in half. If

after drinking from the Fountain, Tina is 16 years old, how old is Ross right now?

7. Carina has 100 ounces of coffee divided into 5- and 10-ounce packages. If she

has 2 more 5-ounce packages than 10-ounce packages, how many 10-ounce

packages does she have?

8. Carla cuts a 70-inch piece of ribbon into 2 pieces. If the first piece is five inches

more than one fourth as long as the second piece, how long is the longer piece

of ribbon?

9. In a used car lot, there are 3 times as many red cars as green cars. If tomorrow

12 green cars are sold and 3 red cars are added, then there will be 6 times as

many red cars as green cars. How many green cars are currently in the lot?

IN ACTION ANSWER KEY

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ManhattanGMATPrep

Chapter 1

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ALGEBRAIC TRANSLATIONS SOLUTIONS

1. 32: Use an age chart to assign variables. Represent Brian’sage now with b. Then John’s age now is b + 20.

Subtract 12 from the “now” column to get the “12 years ago”column.

Then write an equation to represent the remaining information: 12 years ago, John was twice as old asBrian. Solve for b:

b + 8 = 2(b − 12)b + 8 = 2b − 24

32 = b

You could also solve this problem by inspection. John is 20 years older than Brian. We also need John to betwice Brian’s age at a particular point in time. Since John is always 20 years older, then he must be 40 yearsold at that time (and Brian must be 20 years old). This point in time was 12 years ago, so Brian is now 32years old.

2. 45 pounds:Let j = Jackie’s weight, and let s = Stella’s weight. Stella’s weight is the Ultimate Unknown: s = ?

The two dogs weigh a total of 75 pounds. Stella weighs 15 pounds less than twice Jackie’s weight.j + s = 75 s = 2j − 15

Combine the two equations by substituting the value for s from equation (2) into equation (1).j + (2j − 15) = 75

3j − 15 = 753j = 90j = 30

Find Stella’s weight by substituting Jackie’s weight into equation (1).30 + s = 75

s = 45

3. 45 double burgers:Let s = the number of single burgers purchasedLet d = the number of double burgers purchased

Caleb bought 50 burgers: Caleb spent $72.50 in all:s + d = 50 s + 1.5d = 72.50

Combine the two equations by subtracting equation (1) from equation (2).s + 1.5d = 72.50

− (s + d = 50)0.5d = 22.5

d = 45

12 years ago Now

John b + 8 b + 20

Brian b − 12 b = ?

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Retail: $26 Word Translations, Third EditionISBN: 978-0-9818533-7-6

Retail: $26

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1. Number Properties2. Fractions, Decimals, & Percents3. Equations, Inequalities, & VICs4. Word Translations5. Geometry6. Critical Reasoning7. Reading Comprehension8. Sentence Correction

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Third Edition

GMAT® STRATEGY GUIDE

Word Translations

4Guide

Includes Online Access: 6 Computer Adaptive Practice Exams

Bonus Question Bank for Word Translations

See page 7 for details.

How Our GMAT Prep Books Are Different

1. ALGEBRAIC TRANSLATIONS: Translation Techniques, Using Charts, Prices and Quantities, Hidden Constraints

2. RATES & WORK: RTD Charts, Matching Units, Multiple RTD Problems, Average Rate, Basic Work, Working Together, Population, Exponential Growth/Decay (Advanced)

3. RATIOS: Labels, Proportions, Unknown Multipliers, Multiple Ratios

4. COMBINATORICS: Fundamental Counting Principle, Factorials, Anagrams, Multiple Arrangements, Arrangements with Constraints, Combination and Permutation Formulas (Advanced), Disguised Combinatorics (Advanced)

5. PROBABILITY: And vs. Or, 1 – x Shortcut, Domino Effect, Probability Trees, Combinatorics and Probability (Advanced), Combinatorics and Domino Effect (Advanced), Reformulating Difficult Problems (Advanced)

6. STATISTICS: Average Formula, Evenly Spaced Sets, Weighted Averages, Median, Standard Deviation, Shortcuts (Advanced)

7. OVERLAPPING SETS: Double-Set Matrix, Sets & Percents, Sets & Algebraic Representation, Venn Diagrams

8. MINOR PROBLEM TYPES: Optimization, Grouping, Scheduling, Computation, Graphing

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Part of 8-Book Series

What's Inside This Guide

• Clear explanations of fundamental principles.• Step-by-step instructions for important techniques.• Advanced sections covering the most difficult topics.• In-Action practice problems to help you master the concepts and methods.• Topical sets of Official Guide problems listed by number (problems published separately by GMAC) to help you apply your knowledge to actual GMAT questions.• One full year of access to 6 Computer Adaptive Practice Exams and Bonus Question Bank.

• Not just pages of guessing tricks• Real content, real structure, real teaching• More pages per topic than all-in-1 tomes

• Challenges you to do more, not less• Focuses on developing mastery• Covers the subject thoroughly